Bilevel Linear Programming Problems with Quadratic Membership Functions of Fuzzy Parameters

This article considers bilevel linear programming problems where the coefficients of the objective functions in the problem are given as a possibilistic variable characterized by a quadratic membership function. An extended Stackelberg solution is defined by incorporating the notions of possibility theory into the original concept of Stackelberg solutions. The characteristic of the proposed model is that the corresponding Stackelberg problem is exactly solved by using nonlinear bilevel programming techniques.